Title: Raychaudhuri equation: its genesis and significance

Abstract: The Raychaudhuri equation is a geometrical identity. It is particularly useful in gravity theories and helps finding out if there is a focusing of trajectories of particles, indicating a discontinuity (and hence a singularity) in the spacetime geometry. This talk will make an attempt to introduce this equation without much of technicalities for a general audience.

Title: Perturbing the perturbed: Stability of the QNMs for asymptotically de Sitter black holes

Abstract: In this talk, I wish to address the question -- whether the quasi-normal modes, the characteristic frequencies associated with perturbed black hole spacetimes, central to the stability of these black holes, are themselves stable? For this purpose, we have provided a general method of transforming to the hyperboloidal coordinate system, for both asymptotically flat and asymptotically de Sitter spacetimes, which neatly captures the dissipative boundary conditions, and the differential operator becomes non-self-adjoint. Employing the pseudo-spectrum analysis and numerically implementing the same through Chebyshev's spectral method, we present how the quasi-normal modes will drift away from their unperturbed values under external perturbation of the scattering potential. We also discuss the implications of the instability of the fundamental quasi-normal mode on the strong cosmic censorship conjecture.

Title: Testing models beyond ΛCDM

Abstract:  In this talk, I will briefly review the standard cosmological model, and the theoretical and observational challenges that it faces. I will then discuss the need for theories beyond the ΛCDM model and will discuss a few alternatives and the ways to constrain them using different observational probes. 

Title: Thermodynamic (in)stability of Black Holes: A puzzling feature

Abstract: It is well known that for the Kerr-Newman family of black holes there are specific values of J/M^2 and Q/M at which thermodynamic instability sets in. Physically what happens at these ratios is not clear. I will present some preliminary thoughts. This is work in progress.

Title: AKR and Space-time Singularities

Abstract: After the advent of general theory of Relativity by Albert Einstein, much of the effort in subsequent decades was dedicated to mainly solving these very complex equations. Such solutions described the local gravitational fields around compact objects such as blackholes most of the times. The work by Raychaudhuri gave a global view of the dynamical evolutions of matter and geometry in a general manner in the universe for the first time in 1955. His equation described how matter tells spacetime to curve in a general model independent manner. This subsequently played a crucial role in understanding the space-time singularities and their formation, for which Roger Penrose was awarded Nobel prize in 2020. We outline these developments in this talk tracing this exciting cosmic story. 

Title: The Raychaudhuri effect

Abstract: In this talk we will recall the life and work of AKR. This includes discussion on aspects of the Raychaudhuri equation, its consequences ('the Raychaudhuri effect') and applications in diverse areas of physics and mathematics.

Title: Quantum Gravity Effect in Binary Black Hole Merger

Abstract: We present a semi-rigorous justification of Bekenstein’s Generalized Second Law of  Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum Gravity, and considering the inspiral and post-ringdown stages of binary black hole merger into a remnant black hole, we show that the Generalized Second Law implies a lower bound on the non-perturbative LQG correction to the Bekenstein-Hawking area law for black hole entropy. This lower bound itself is expressed as a function of the Bekenstein-Hawking area formula for entropy. Using the analyses of LIGO-VIRGO-KAGRA data recently performed to verify the Hawking Area Theorem for binary black hole merger, this Loop Quantum Gravity-induced lower bound is shown to be entirely consistent with the data.

Title: AKR and the teaching of physics

Abstract: I was fortunate to have AKR as my teacher during both my BSc and MSc studies.  I will recall some memories of his classes, and also of some incidents that happened outside the class.  I was one of the persons who took class notes during his MSc class on Classical Mechanics.  These notes later came out as a book.  I will present some recollections of this period.  In the last part of my talk, I will discuss what I have learned from AKR and some other great teachers about teaching, and what are the new things that we have to think of in the light of developments that took place since their times.

Title: Reviving the Stueckelberg Mechanism

Abstract: In the 1950s, Stueckelberg invented an elegant mechanism to give mass to gauge bosons without breaking the gauge symmetry. However, the model was abandoned for some technical reasons, and instead a spontaneous symmetry-breaking model based on the older Ginzburg-Landau theory became the cornerstone of the Standard Model. This has now been vindicated by the discovery of the Higgs boson. Nevertheless, the Stueckelberg mechanism remains a powerful tool in extensions of the Standard Model. One such example, with a minimal U(1) gauge extension, is studied in detail and a model is obtained which is both phenomenologically viable and economic. This talk will first review the Stueckelberg mechanism and then describe its contemporary application.

Title: Raychaudhuri Equation: Classical, Thermodynamic & Quantum

Abstract: In this talk, I will describe different aspects of the famous Raychaudhuri equation for classical black hole mechanics, semi-classical black hole thermodynamics, and perturbative quantum gravity.

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Title: A journey to the wonderland of hidden dimensions

Abstract: We believe that we live in a world of 3 spatial dimensions and inevitably flow towards the future with time. Modifying the Newtonian concept of absolute time, Einstein proposed a  revolutionary understanding  of (3 + 1 ) dimensional space and time through the Special and General theory of Relativity. But can there be more  invisible dimension(s)  which may explain so many unexplained phenomena that puzzle us for a long time ? If yes then what is the nature of this hidden world ? Why are these dimensions invisible ? What could be the possible  direct or indirect evidence in favour of their existence ?

This talk will be a journey to this hidden wonderland.

Title: Loop contributions to the scalar power spectrum due to quartic order action in ultra slow roll inflation

Abstract: Recently, there have been efforts to examine the contributions to the scalar power spectrum due to the loops arising from the cubic order terms in the action describing the perturbations, specifically in inflationary scenarios that permit a brief epoch of ultra slow roll (USR). A phase of USR inflation leads to significant observational consequences, such as the copious production of primordial black holes and the generation of secondary gravitational waves of observable amplitudes. In this talk, I shall discuss the loop contributions to the scalar power spectrum in scenarios of USR inflation arising due to the quartic order terms in the action describing the scalar perturbations. I shall initially describe the computation of the loop contributions to the scalar power spectrum due to the dominant term in the action at the quartic order. Thereafter, I shall consider a scenario wherein a phase of USR is sandwiched between two stages of slow roll inflation and describe the behavior of the loop contributions in situations involving late, intermediate and early epochs of USR. In the inflationary scenario involving a late phase of USR, for reasonable choices of the parameters, I shall show that the loop corrections are negligible for the entire range of wave numbers. In the intermediate case, the contributions from the loops prove to be scale invariant over large scales, and we find that these contributions can amount to 30% of the power spectrum at the leading order. In the case wherein USR sets in early, we find that the loop contributions could be negative and can dominate the power spectrum at the leading order, which indicates a breakdown of the perturbative expansion. I shall conclude with a brief summary and outlook.

Title: AKR and the laws of black hole mechanics

Abstract: Using the famous Raychaudhuri equations, I will show that a non-trivial first law for Rindler horizons exists. I will also discuss issues related to the second law, specifically in what situations the second law can be established (for black holes and Rindler horizons) using Raychaudhuri equations.

Title: Dynamics of Black Hole Evaporation in 2-dim Gravity: A Study using the dual SYK Model coupled to a bath

Abstract: We will discuss the non-equilibrium dynamics of a low temperature 2-dim black hole coupled to an external bath, using the dual SYK model. Tracing over the bath degrees of freedom, in the Schwinger-Keldysh formalism, leads to solving non-local stochastic differential equations for the BH degrees of freedom. We describe the combination of SYK operators that enable complete evaporation of the BH, and the fluctuations that characterise the end point of the evaporation process. This talk is based on JHEP 08 (2023) 171 (arXiv:2210.15579).